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A rapid method for assessing the quality of sieves
Powd:=r Technology. 13 (1976) 97 - 101 0 Elsevier Sequoia S-A., Lausanne - Printed in the Netherlands
A Rapid Method
for Assessing
H. KONO\VALCHUK*, Physics Department. (Received
the Quality
A. G. NAYLOR Laurentian
97
of Sieves
and B. H. KAYE
University.
Sudbury.
Ont. (Canada)
May 19, 1975)
SUMMARY
It is shown that optical processing using amplitude spatial filtering can speed up the process of assessing the quality of a sieve. The optical processing technique operates on a large number of apertures in parallel and not sequentially as with a microscope measurement method, and it enhances the damaged or distorted area of the sieve. Thus it is much easier with this method than with the microscope method to locate the damaged region and make quantitative measurements of the damage.
INTRODUCTION
Sieves are used extensively in industry to prepare powders whose individual particles lie within a certain size range, the size range depending on the nature of the powder and the use to which it will be put. Sieving is also a standard technique for measuring the size range of particles in a powder system. The size of the openings in the sieves mostly fall within the range 5 - 200 pm. The sieves themselves fall into two basic categories: (1) wirewoven sieves, (2) electroformed sieves_ The wire-woven sieves are generally restricted to mesh size of 37 pm and greater. The electroformed sieves are made down to mesh sizes of 5 pm and could be made with smaller mesh sizes when the demand occ-urs, because the technology is already developed. The mesh of the electroformed sieves is usually supported on a grid, while the wire-woven sieves are selfsupporting. Sieve cloth is expensive and its cost rises as the mesh size gets smaller, and
*Present address: Falconbridge Sudbury, Ont., Canada.
Nickel Mines,
electroformed sieves in particular are very expensive. To prepare powders with a certain size distribution, or to measure the size distribution of a powder, the mesh apertures in the sieve must lie within defined limits. If the sieve cloth becomes worn the apertures may become enlarged, smaller, or blocked. If the apertures become larger or smaller this will lead to powder samples with incorrect size distribution, and if the apertures become blocked the efficiency of the sieving process is lessened. In practice it is a difficult job to decide when to replace the sieve, because the apertures are too small to be seen individually by the eye and there are so many of them. At the present time the checking is done by inspecting each aperture of the sieve or a random selection of apertures with a microscope. This is very time-consuming, and it is therefore usually cheaper to replace the sieve after a given period of time, this period of time being determined empirically. Just as there is no simple method of checking the sieves after they have been used, there is no simple method of checking them before they are used, and no simple metllod of quality control in the production of sieve cloth. By the nature of the processes involved in making the sieves, the inaccuracies in the mesh sizes of woven sieve cloth are much greater than in electroformed sieve ‘Lcloth”. The sieve can be looked upon as a twodimensional periodic grating, and hence optical processing techniques can be used in trying to obtain an efficient method of assessing the quality of a new or used sieveFor example, Will and Pennington [l] used spatial filtering to obtain defect enhancement in semiconductor wafers, which pose the same type of problem, i-e_ many of them and smallness. The electroformed sieves approximate very well to a two-dimensional aperture, but the weaving process leaves the
wire-wosen sieve cloth with a more pronounced third dimension_ X similar problem to the case of wire-woven sieves was considered theoretically by Bell and Romero [ 21 using Iarger apertures and infrared wavelengths, and it was shown that diffraction theory could be used to a good approsimation The purpose of the work described here is to demonstrate that optical processing can he used to assess the qualit>- of new or used sieves.
ESPERIXIES-I’_AL
PROCEDURE
The esperimental arrangement is shown in Fig_ 1, which is the standard arrangement for spatial filtering [ 3]_ The Fraunhofer diffraction pattern of the sieve is fomied by lens L, in the back focal plane of the lens. The Fraunhofer diffraction pattern of an object can be shown to be the Fourier transform of that object, and the plane in which it is formed IS known as the transform plane_ It can also be shown that if the object consists of two par-~ f(s.y) and g(.x.y), ((.r.y) are coordinates in the object plane), then the lens will form the Fourier transform F(u_u_) and G(n_u_), ((rr.t=) are coordinates in the transform plane) in the transform plane. If another lens Ls is. plxed such that its front focal plane coincides with the transform plane of lens L,, then the lens L, will perform another transform creating an image in the back focal plane of the original oblect, but the object will be inverted and reversed_ If the energy due to fl_r,y) is blocked. and the energy due to g(s,y) is used to reform the image, then only an image of g(x,y) will occur. If we assume that f(x,y) represents the undistorted or damaged part, and if the spatial frequencies in the Fourier transform of the undistorted part do not overlap greatly, then a simple binary amplitude filter can be used. If the spatial frequen-
ties do overlap, an amplitude/phase filter would have to be used. It will be shown that sufficient enhancement of the distorted part of the object is obtained using a binary amplitude filter only_ The beam from a 2 milliwatt He-Ne laser was filtered and expanded to a diameter of approximately 3 cm before being collimated. This was obtained by placing lens L a distance equal to its focal length (25 cm) away from a pinhole. The beam was not large enough to cover the whole of the sieve cloth under test. The sieves used were 8 in_ standard Tyler wire-woven sieves. _A suggested method of scanning the whole sieve will be discussed later. The “binary” amplitude filter was constructed in the first place on a photographic film; hence it was not strictly binary, as even a saturated photographic film will allow some light to pass through it, and shouid strictly be called an amplitude filter. In order to construct the filter, an undamaged sieve should be used. Even a new sieve may be damaged as far as the ideal sieve is concerned, but it was shown by Will and Bennington [1] that it is possible to make a filter using a relatively small area which can be considered ideal_ The difference in the filter formed by using a small area and a much larger area is very small, because even a small area will contain a large number of apertures_ The difference between the Fourier transform of a large number of regularly spaced apertures and the Fourier transform of a very large number of regularly spaced apertures is small [4] _ Thus an area of sieves with “ideal” apertures can be selected by observing the sieve with a microscope. Once the filter is made for these “ideal” apertures, it can be used indefinitely for assessing the damage and distortion to a sieve whose apertures are supposed to be equal to
99 12345
ALONG
LIN
E
b-b
IIIII
-a b-
Fig. 3. Filtered image of wire-woven
sieve.
that of the “ideal” apertures. It is relatively easy to determine theoretically the diffraction pattern for a regular array of apertures [ 4 J , so that a true binary filter could be constructed by placing an opaque dot in the appropriate positions on a transparent screen. The area containing the ideal apertures was placed in the beam at the input plane, and a Kodak 649F holographic pIate was mounted in the filter plane. The intensity distribution of the Fourier transform of the apertures was recorded on the photographic plate. These types of plates are slow, so the system had to be free of vibration during the exposure- These plates were used because of the high optical density avaiIabIe with them, and because glass plates are much easier to relocate in a given position than is sheet film. The high resolution of these plates is not essential for making this type of amplitude filter, so any high-contrast glass-mounted emulsion would be suitable_
Fig. 4. Fourier transform
of regular array.
The lenses used in this work were simple single-element lenses of focal length 25 cm, so the plate or film did not need to have a resolution of more than 100 lines/mm. If one is trying to de*zrmine very small defects in an object, then higher resolution films and better quality lenses would be required. A typical section of a wire-woven 105 pm Tyler sieve is shown in Fig. 2. There is obvious damage to the sieve just to the upper left of centre, but closer inspection will reveal smaller amounts of damage in the far upper left and lower right. This becomes obvious when inspecting the filtered image shown in Fig. 3. From inspecting such a filtered image as this, one can immediately make rapid qualitative decisions as to the quality of that piece of the sieve, whereas inspection of Fig. 2 would take much longer to find the damaged areas. With an adequate scanning system an operator could rapidly
10
n
rL
Fig_ 5_ Filtered image with low pass.
assess the quality of a sieve at least qualitatively by visual inspection alone, which for many applications would be all that is required. A reguIar array of a large number of apertures produces a Fourier transform which contains a large high spatial frequency component_ Figure 4 shows the Fourier transform of a reguiar array of a large number of square apertures- The Fourier transform of the damaged areas, which can be taken (as a fmt approximation) to be randomly spaced apertures of random size, will in general contain much lower frequencies than tine array of apertures- Hence a further suppression of the reguIar array in the reconstructed image can be obtained by placing an aperture stop in the filter plane to allow only the lowfrequency components to pass. This leads to an improvement in the enhancement of the distorted parts, as shown in Fig. 5. So far only qualitative results have been considered. To obtain some idea as to the minimum extent of distortion which can be detected, a fiber optic scanning system was @aced in the reconstructed image plane. The fiber optic scanning system consisted of a flexible fiber optic bundle with an aperture of approximately 50 pm- The output from the photomultiplier was linked to a chart recorder_ The aperture end of the fiber optic bundle could be driven at constant speed in an x direction. hence a plot of intensity as a function of position in the image pIane along the x direction, for a fiied y position, could be
ob’;ained. The chart readouts are shown in Fig. 6 from scans along ‘a - a’, ‘b - b’ and ‘c - C’ of Fig. 2 (with the filter in position
POSlTlON
Fig. 6. Intensity lines
lCONG
as a function
c--c
of
position
along scan
without filtering and with filtering). The areas of the damaged aperture in region b - b are shown in Table 1. The area of aperture 3 corresponded to a side of 125 pm or an enlargement of approximately 2070, while the area of aperture 2 corresponded to a side of 97 pm or a reduction in area of approximately 8% The two peaks A and B in Fig. 6 correspond to the apertures 2 and 3 as shown in Fig. 2. There is obviously a relationship between the difference in the size of the distorted apertures and the ideal aperture, but no attempt has been made to determine exactly what the relationship is. The reason for this is that the area or the related length of one side of the aperture is not necessarily a good measure of the quality of the sieve. The TABLE
1
Area of apertures 1 to 5 along line b - b Aperture
Area
1 2 3 4 5
12-5 10.5 16.7 11.1 11.9
(X10-a
m*)
101
L
I5
,
I
I
I
IO
5
0
5
ANGULAR
Fig_ 7. Intensity
1
IO
15
ORIENTATION
passed by filter as a function
of fiIter orientation.
type of powder which is being used with a particu1a.r sieve wilI determine which dimension of the size is important_ In generaI the particles are regarded as sphericai,*and the minimum aperture dimension of the sieve is then important; however, for elongated particies both the minimum and maximum aperture dimensions are important. A decision has to be made on what dimensions of a sieve are important and then relate the intensity in the image plane to the damage. It should be pointed out that at the present time the decision as to whether a sieve is “good” or “damaged” is based on very qualitative judgements and with assessment of only a small area of the sieve, so a number count of the bright spots in the filtered image with intensities over a set minimum will give a quantitative judgement of the quality of the sieve. This will be a great impro*rament over the present methods. The amount of sieve which could be assessed with the method so far described depends on the size of the beam, which in turn is Iimited by the diameter and quality of the lenses used. Larger areas could be observed using larger lenses; however, it is uniikely that one would consider the expense of a lens large enough to view the whole of an 8 in. sieve worthwhile. The equipment would prove to be too expensive. The sieve has therefore to be scanned using a relatively small beam. A simple system would be to move the sieve, but care has to be taken to prevent the sieve from rotating, as the Nter is angle-dependent. This is illustrated in Fig. 7, where the intensity in the regular filtered image is plotted as a function of the angular orientation of the sieve
to the filter. It can be seen that the intensity in the regular image rises rapidly for small changes in orientation, thus lowering the contrast between regular image pattern and the damage pattern. The necessary machining tolerances on moving slides are easily obtained, so provided the sieve is well aligned with the filter initially, it can be driven automatically in an -r,y plane in such a way that the whole sieve can be scanned- A spiral scan starting at the centre may be more convenient mechanically than an _r,y scan, but in this case the filter must also be rotated and the interpretation of the image becomes more difficult unless compensation is made for rotation of the image. CONCLUSION
This method of spatial filtering provides a rapid detailed assessment of the quality of a sieve. The results given are for a 105 I.rrn wirewoven sieve; the same theory will hold for sieve apertures as low as 3 pm, but the light intensities in the image plane will be low. Work is proceeding on automating the system so that a whole sieve may be scanned. REFERENCES P_ M. Will and K S. Pennington, Appi_ Opt., 9 (1971) 2097 - 2100. R. J. Bell and K V. Romero, Appl. Opt., 9 (1970) 23412349. J. W. Goodman, Introduction to Fourier Optics, McGraw Hill, New York, 1968. J. U Stone, Radiation and Optics, McGraw-Hill, New York, 1963.
A Rapid Method
for Assessing
H. KONO\VALCHUK*, Physics Department. (Received
the Quality
A. G. NAYLOR Laurentian
97
of Sieves
and B. H. KAYE
University.
Sudbury.
Ont. (Canada)
May 19, 1975)
SUMMARY
It is shown that optical processing using amplitude spatial filtering can speed up the process of assessing the quality of a sieve. The optical processing technique operates on a large number of apertures in parallel and not sequentially as with a microscope measurement method, and it enhances the damaged or distorted area of the sieve. Thus it is much easier with this method than with the microscope method to locate the damaged region and make quantitative measurements of the damage.
INTRODUCTION
Sieves are used extensively in industry to prepare powders whose individual particles lie within a certain size range, the size range depending on the nature of the powder and the use to which it will be put. Sieving is also a standard technique for measuring the size range of particles in a powder system. The size of the openings in the sieves mostly fall within the range 5 - 200 pm. The sieves themselves fall into two basic categories: (1) wirewoven sieves, (2) electroformed sieves_ The wire-woven sieves are generally restricted to mesh size of 37 pm and greater. The electroformed sieves are made down to mesh sizes of 5 pm and could be made with smaller mesh sizes when the demand occ-urs, because the technology is already developed. The mesh of the electroformed sieves is usually supported on a grid, while the wire-woven sieves are selfsupporting. Sieve cloth is expensive and its cost rises as the mesh size gets smaller, and
*Present address: Falconbridge Sudbury, Ont., Canada.
Nickel Mines,
electroformed sieves in particular are very expensive. To prepare powders with a certain size distribution, or to measure the size distribution of a powder, the mesh apertures in the sieve must lie within defined limits. If the sieve cloth becomes worn the apertures may become enlarged, smaller, or blocked. If the apertures become larger or smaller this will lead to powder samples with incorrect size distribution, and if the apertures become blocked the efficiency of the sieving process is lessened. In practice it is a difficult job to decide when to replace the sieve, because the apertures are too small to be seen individually by the eye and there are so many of them. At the present time the checking is done by inspecting each aperture of the sieve or a random selection of apertures with a microscope. This is very time-consuming, and it is therefore usually cheaper to replace the sieve after a given period of time, this period of time being determined empirically. Just as there is no simple method of checking the sieves after they have been used, there is no simple method of checking them before they are used, and no simple metllod of quality control in the production of sieve cloth. By the nature of the processes involved in making the sieves, the inaccuracies in the mesh sizes of woven sieve cloth are much greater than in electroformed sieve ‘Lcloth”. The sieve can be looked upon as a twodimensional periodic grating, and hence optical processing techniques can be used in trying to obtain an efficient method of assessing the quality of a new or used sieveFor example, Will and Pennington [l] used spatial filtering to obtain defect enhancement in semiconductor wafers, which pose the same type of problem, i-e_ many of them and smallness. The electroformed sieves approximate very well to a two-dimensional aperture, but the weaving process leaves the
wire-wosen sieve cloth with a more pronounced third dimension_ X similar problem to the case of wire-woven sieves was considered theoretically by Bell and Romero [ 21 using Iarger apertures and infrared wavelengths, and it was shown that diffraction theory could be used to a good approsimation The purpose of the work described here is to demonstrate that optical processing can he used to assess the qualit>- of new or used sieves.
ESPERIXIES-I’_AL
PROCEDURE
The esperimental arrangement is shown in Fig_ 1, which is the standard arrangement for spatial filtering [ 3]_ The Fraunhofer diffraction pattern of the sieve is fomied by lens L, in the back focal plane of the lens. The Fraunhofer diffraction pattern of an object can be shown to be the Fourier transform of that object, and the plane in which it is formed IS known as the transform plane_ It can also be shown that if the object consists of two par-~ f(s.y) and g(.x.y), ((.r.y) are coordinates in the object plane), then the lens will form the Fourier transform F(u_u_) and G(n_u_), ((rr.t=) are coordinates in the transform plane) in the transform plane. If another lens Ls is. plxed such that its front focal plane coincides with the transform plane of lens L,, then the lens L, will perform another transform creating an image in the back focal plane of the original oblect, but the object will be inverted and reversed_ If the energy due to fl_r,y) is blocked. and the energy due to g(s,y) is used to reform the image, then only an image of g(x,y) will occur. If we assume that f(x,y) represents the undistorted or damaged part, and if the spatial frequencies in the Fourier transform of the undistorted part do not overlap greatly, then a simple binary amplitude filter can be used. If the spatial frequen-
ties do overlap, an amplitude/phase filter would have to be used. It will be shown that sufficient enhancement of the distorted part of the object is obtained using a binary amplitude filter only_ The beam from a 2 milliwatt He-Ne laser was filtered and expanded to a diameter of approximately 3 cm before being collimated. This was obtained by placing lens L a distance equal to its focal length (25 cm) away from a pinhole. The beam was not large enough to cover the whole of the sieve cloth under test. The sieves used were 8 in_ standard Tyler wire-woven sieves. _A suggested method of scanning the whole sieve will be discussed later. The “binary” amplitude filter was constructed in the first place on a photographic film; hence it was not strictly binary, as even a saturated photographic film will allow some light to pass through it, and shouid strictly be called an amplitude filter. In order to construct the filter, an undamaged sieve should be used. Even a new sieve may be damaged as far as the ideal sieve is concerned, but it was shown by Will and Bennington [1] that it is possible to make a filter using a relatively small area which can be considered ideal_ The difference in the filter formed by using a small area and a much larger area is very small, because even a small area will contain a large number of apertures_ The difference between the Fourier transform of a large number of regularly spaced apertures and the Fourier transform of a very large number of regularly spaced apertures is small [4] _ Thus an area of sieves with “ideal” apertures can be selected by observing the sieve with a microscope. Once the filter is made for these “ideal” apertures, it can be used indefinitely for assessing the damage and distortion to a sieve whose apertures are supposed to be equal to
99 12345
ALONG
LIN
E
b-b
IIIII
-a b-
Fig. 3. Filtered image of wire-woven
sieve.
that of the “ideal” apertures. It is relatively easy to determine theoretically the diffraction pattern for a regular array of apertures [ 4 J , so that a true binary filter could be constructed by placing an opaque dot in the appropriate positions on a transparent screen. The area containing the ideal apertures was placed in the beam at the input plane, and a Kodak 649F holographic pIate was mounted in the filter plane. The intensity distribution of the Fourier transform of the apertures was recorded on the photographic plate. These types of plates are slow, so the system had to be free of vibration during the exposure- These plates were used because of the high optical density avaiIabIe with them, and because glass plates are much easier to relocate in a given position than is sheet film. The high resolution of these plates is not essential for making this type of amplitude filter, so any high-contrast glass-mounted emulsion would be suitable_
Fig. 4. Fourier transform
of regular array.
The lenses used in this work were simple single-element lenses of focal length 25 cm, so the plate or film did not need to have a resolution of more than 100 lines/mm. If one is trying to de*zrmine very small defects in an object, then higher resolution films and better quality lenses would be required. A typical section of a wire-woven 105 pm Tyler sieve is shown in Fig. 2. There is obvious damage to the sieve just to the upper left of centre, but closer inspection will reveal smaller amounts of damage in the far upper left and lower right. This becomes obvious when inspecting the filtered image shown in Fig. 3. From inspecting such a filtered image as this, one can immediately make rapid qualitative decisions as to the quality of that piece of the sieve, whereas inspection of Fig. 2 would take much longer to find the damaged areas. With an adequate scanning system an operator could rapidly
10
n
rL
Fig_ 5_ Filtered image with low pass.
assess the quality of a sieve at least qualitatively by visual inspection alone, which for many applications would be all that is required. A reguIar array of a large number of apertures produces a Fourier transform which contains a large high spatial frequency component_ Figure 4 shows the Fourier transform of a reguiar array of a large number of square apertures- The Fourier transform of the damaged areas, which can be taken (as a fmt approximation) to be randomly spaced apertures of random size, will in general contain much lower frequencies than tine array of apertures- Hence a further suppression of the reguIar array in the reconstructed image can be obtained by placing an aperture stop in the filter plane to allow only the lowfrequency components to pass. This leads to an improvement in the enhancement of the distorted parts, as shown in Fig. 5. So far only qualitative results have been considered. To obtain some idea as to the minimum extent of distortion which can be detected, a fiber optic scanning system was @aced in the reconstructed image plane. The fiber optic scanning system consisted of a flexible fiber optic bundle with an aperture of approximately 50 pm- The output from the photomultiplier was linked to a chart recorder_ The aperture end of the fiber optic bundle could be driven at constant speed in an x direction. hence a plot of intensity as a function of position in the image pIane along the x direction, for a fiied y position, could be
ob’;ained. The chart readouts are shown in Fig. 6 from scans along ‘a - a’, ‘b - b’ and ‘c - C’ of Fig. 2 (with the filter in position
POSlTlON
Fig. 6. Intensity lines
lCONG
as a function
c--c
of
position
along scan
without filtering and with filtering). The areas of the damaged aperture in region b - b are shown in Table 1. The area of aperture 3 corresponded to a side of 125 pm or an enlargement of approximately 2070, while the area of aperture 2 corresponded to a side of 97 pm or a reduction in area of approximately 8% The two peaks A and B in Fig. 6 correspond to the apertures 2 and 3 as shown in Fig. 2. There is obviously a relationship between the difference in the size of the distorted apertures and the ideal aperture, but no attempt has been made to determine exactly what the relationship is. The reason for this is that the area or the related length of one side of the aperture is not necessarily a good measure of the quality of the sieve. The TABLE
1
Area of apertures 1 to 5 along line b - b Aperture
Area
1 2 3 4 5
12-5 10.5 16.7 11.1 11.9
(X10-a
m*)
101
L
I5
,
I
I
I
IO
5
0
5
ANGULAR
Fig_ 7. Intensity
1
IO
15
ORIENTATION
passed by filter as a function
of fiIter orientation.
type of powder which is being used with a particu1a.r sieve wilI determine which dimension of the size is important_ In generaI the particles are regarded as sphericai,*and the minimum aperture dimension of the sieve is then important; however, for elongated particies both the minimum and maximum aperture dimensions are important. A decision has to be made on what dimensions of a sieve are important and then relate the intensity in the image plane to the damage. It should be pointed out that at the present time the decision as to whether a sieve is “good” or “damaged” is based on very qualitative judgements and with assessment of only a small area of the sieve, so a number count of the bright spots in the filtered image with intensities over a set minimum will give a quantitative judgement of the quality of the sieve. This will be a great impro*rament over the present methods. The amount of sieve which could be assessed with the method so far described depends on the size of the beam, which in turn is Iimited by the diameter and quality of the lenses used. Larger areas could be observed using larger lenses; however, it is uniikely that one would consider the expense of a lens large enough to view the whole of an 8 in. sieve worthwhile. The equipment would prove to be too expensive. The sieve has therefore to be scanned using a relatively small beam. A simple system would be to move the sieve, but care has to be taken to prevent the sieve from rotating, as the Nter is angle-dependent. This is illustrated in Fig. 7, where the intensity in the regular filtered image is plotted as a function of the angular orientation of the sieve
to the filter. It can be seen that the intensity in the regular image rises rapidly for small changes in orientation, thus lowering the contrast between regular image pattern and the damage pattern. The necessary machining tolerances on moving slides are easily obtained, so provided the sieve is well aligned with the filter initially, it can be driven automatically in an -r,y plane in such a way that the whole sieve can be scanned- A spiral scan starting at the centre may be more convenient mechanically than an _r,y scan, but in this case the filter must also be rotated and the interpretation of the image becomes more difficult unless compensation is made for rotation of the image. CONCLUSION
This method of spatial filtering provides a rapid detailed assessment of the quality of a sieve. The results given are for a 105 I.rrn wirewoven sieve; the same theory will hold for sieve apertures as low as 3 pm, but the light intensities in the image plane will be low. Work is proceeding on automating the system so that a whole sieve may be scanned. REFERENCES P_ M. Will and K S. Pennington, Appi_ Opt., 9 (1971) 2097 - 2100. R. J. Bell and K V. Romero, Appl. Opt., 9 (1970) 23412349. J. W. Goodman, Introduction to Fourier Optics, McGraw Hill, New York, 1968. J. U Stone, Radiation and Optics, McGraw-Hill, New York, 1963.